Elliptical vortex and oblique vortex lattice in the FeSe superconductor based on the nematicity and mixed superconducting orders

Abstract

The electronic nematic phase is characterized as an ordered state of matter with rotational symmetry breaking, and has been well studied in the quantum Hall system and the high-T_c superconductors, regardless of cuprate or pnictide family. The nematic state in high-T_c systems often relates to the structural transition or electronic instability in the normal phase. Nevertheless, the electronic states below the superconducting transition temperature is still an open question. With high-resolution scanning tunneling microscope measurements, direct observation of vortex core in FeSe thin films revealed the nematic superconducting state by Song et al. Here, motivated by the experiment, we construct the extended Ginzburg–Landau free energy to describe the elliptical vortex, where a mixed s-wave and d-wave superconducting order is coupled to the nematic order. The nematic order induces the mixture of two superconducting orders and enhances the anisotropic interaction between the two superconducting orders, resulting in a symmetry breaking from C₄ to C₂. Consequently, the vortex cores are stretched into an elliptical shape. In the equilibrium state, the elliptical vortices assemble a lozenge-like vortex lattice, being well consistent with experimental results.

Superconductivity: multiple orders couple to produce elliptical vortex

Theorists construct the extended Ginzburg-Landau free energy to explain the elliptical superconducting vortex, where multiple orders are coupled. A team led by Da-Chuan Lu and Jun Li from Nanjing University in China theoretically studied the nematic superconducting state, which is characterized by elliptical vortices, reported in a recent experiment. They construct the extended Ginzburg-Landau free energy by implementing finite element method to the time-dependent Ginzburg-Landau equations with open boundary conditions. The method describes the elliptical vortex, where a mixing of superconducting orders couple with a nematic order. The coupling further enhances the anisotropic interaction between superconducting orders and results in a four-fold to two-fold rotational symmetry breaking. The elliptical vortices assemble a lozenge-like vortex lattice, which is consistent with experimental results.